The Dutch cellist, Anner Bylsma [Bijlsma], received his first lessons were from a parent, in this case his father, also a multi-talented musician. At the age of 16, he enrolled at the Royal Conservatory, The Hague, to study with Carel van Leeuwen Boomkamp, principal cellist with the Concertgebouw Orchestra Amsterdam. It was Boomkamp who introduced Bylsma to the Baroque cello. Bylsma won the school's Prix d'excellence in 1957, and after becoming the Netherlands Opera Orchestra's principal cellist, he won first prize in the Casals Competition in Mexico in 1959.

Anner Bylsma became an Erasmus Scholar at Harvard University in 1982. He is also a noted scholar and teacher and author of Bach - The Fencing Master, a stylistic and aesthetic analysis of the first three of J.S. Bach's Cello Suites. His playing is always based on what he finds in the composers' manuscripts. However, he quickly admits that his interpretation of a work is not and should not be the only one, which he also impresses on his students. Although he doesn't like to use the term "authentic," it is in keeping with period performance that he avoids the use of steel strings, and this is a major element of his tone. Both his 1695 Gofriller cello and his 1865 Pressenda are strung with gut or silver-wrapped gut. He also has a five-string "violoncello piccolo" that he has used to record J.S. Bach's solo works.

His recordings can be found on a variety of labels, covering a variety of works, from Antonio Vivaldi to Paul Hindemith. In 1979 Bijlsma recorded the Six Suites for unaccompanied cello (BWV 1007-1012) by J.S. Bach, the first of its kind on a period instrument. He also made a second recording of the same music in 1992 on the large Servais Stradivarius and on a five-string violoncello piccolo. Many of his recordings on Sony, both as a soloist and with L'Archibudelli, have won the Edison prize, the Diapason d'or, the Liszt prize, and the Vivaldi prize.